Question

suppose that a sequence is defined as follows.
$a_1 = -4$, $a_n = 3a_{n - 1} + 7$ for $n \geq 2$
list the first four terms of the sequence.

Explanation:

Step1: Identify first term

$a_1 = -4$

Step2: Calculate second term

Substitute $n=2$: $a_2 = 3a_1 + 7 = 3(-4) + 7 = -12 + 7 = -5$

Step3: Calculate third term

Substitute $n=3$: $a_3 = 3a_2 + 7 = 3(-5) + 7 = -15 + 7 = -8$

Step4: Calculate fourth term

Substitute $n=4$: $a_4 = 3a_3 + 7 = 3(-8) + 7 = -24 + 7 = -17$

Answer:

$-4, -5, -8, -17$